The Herman-Kluk (HK) semiclassical propagator is applied to two-dimensional (2D) and four-dimensional (4D) activated reactive scattering of H-2 from a Cu(100) surface. Flux analysis is used to calculate collision-energy-dependent reaction probabilities from the time dependence of the semiclassical wave function; several different variations of this analysis method are implemented. Direct comparison is made between the reaction probabilities calculated using the HK method, and numerically exact quantum results, as well as quasiclassical (QC) trajectory calculations. Although aspects of results obtained using the HK propagator are an improvement over the QC results-for example, reproduction of the quantum reaction threshold and quantum resonances-overall the HK reaction probabilities are no more accurate than the QC probabilities. Furthermore, the HK method is relatively expensive to apply, and the computational expense does not scale with dimension as favorably as might be expected. The reasons for this are discussed.